Best Known (247−72, 247, s)-Nets in Base 2
(247−72, 247, 138)-Net over F2 — Constructive and digital
Digital (175, 247, 138)-net over F2, using
- 21 times duplication [i] based on digital (174, 246, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 82, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- trace code for nets [i] based on digital (10, 82, 46)-net over F8, using
(247−72, 247, 229)-Net over F2 — Digital
Digital (175, 247, 229)-net over F2, using
(247−72, 247, 1607)-Net in Base 2 — Upper bound on s
There is no (175, 247, 1608)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 229 177522 420096 968489 841654 428507 085832 920795 597819 866506 395919 340868 841682 > 2247 [i]